Ta có: \(AM=\frac12\times AB\)

=>\(S_{DMA}=\frac12\times S_{DAB}\)

Ta có: \(AQ=\frac12\times AD\)

=>\(S_{AMQ}=\frac12\times S_{ADM}=\frac14\times S_{ADB}\)

Ta có: \(CN=\frac12\times CB\)

=>\(S_{DNC}=\frac12\times S_{DBC}\)

Ta có: \(CP=\frac12\times CD\)

=>\(S_{PCN}=\frac12\times S_{DNC}=\frac12\times\frac12\times S_{DBC}=\frac14\times S_{DBC}\)

Ta có: \(BN=\frac12\times BC\)

=>\(S_{ABN}=\frac12\times S_{ABC}\)

Ta có: \(BM=\frac12\times BA\)

=>\(S_{BMN}=\frac12\times S_{BMC}=\frac14\times S_{ABC}\)

Ta có: \(DP=\frac12\times DC\)

=>\(S_{DAP}=\frac12\times S_{DAC}\)

\(DQ=\frac12\times DA\)

=>\(S_{DQP}=\frac12\times S_{DPA}=\frac12\times\frac12\times S_{DAC}=\frac14\times S_{DAC}\)

Ta có: \(S_{AMQ}+S_{BMN}+S_{CNP}+S_{DQP}+S_{MNPQ}=S_{ABCD}\)

=>\(S_{MNPQ}+\frac14\times\left(S_{ABC}+S_{ADC}\right)+\frac14\times\left(S_{ABD}+S_{CBD}\right)=S_{ABCD}\)

=>\(S_{MNPQ}=\frac12\times S_{ABCD}=\frac12\times100=50\left(\operatorname{cm}^2\right)\)

Ta có: \(ME=\frac12\times MN\)

=>\(S_{QEM}=\frac12\times S_{QMN}\)

Ta có: \(MH=\frac12\times MQ\)

=>\(S_{MHE}=\frac12\times S_{QME}=\frac14\times S_{MQN}\)

Ta có: \(PG=\frac12\times PQ\)

=>\(S_{NGP}=\frac12\times S_{NPQ}\)

Ta có: \(PF=\frac12\times PN\)

=>\(S_{PGF}=\frac12\times S_{PGN}=\frac14\times S_{PQN}\)

Ta có: \(QH=\frac12\times QM\)

=>\(S_{QHP}=\frac12\times S_{QMP}\)

Ta có: \(QG=\frac12\times QP\)

=>\(S_{GHQ}=\frac12\times S_{QHP}=\frac14\times S_{QMP}\)

Ta có: \(NE=\frac12\times NM\)

=>\(S_{PEN}=\frac12\times S_{PMN}\)

Ta có: \(NF=\frac12\times NP\)

=>\(S_{NFE}=\frac12\times S_{NEP}=\frac12\times\frac12\times S_{NMP}=\frac14\times S_{NMP}\)

Ta có: \(S_{NFE}+S_{MHE}+S_{QHG}+S_{PGF}+S_{EHGF}=S_{MNPQ}\)

=>\(S_{EHGF}=S_{MNPQ}-\frac14\times\left(S_{MQN}+S_{PQN}\right)-\frac14\times\left(S_{NMP}+S_{QMP}\right)\)

=>\(S_{EHGF}=S_{MNPQ}-\frac14\times S_{MNPQ}-\frac14\times S_{MNPQ}=\frac12\times S_{MNPQ}\)

\(=\frac12\times50=25\left(\operatorname{cm}^2\right)\)